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On a relative uniform completion of an archimedean lattice ordered group

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Mathematica Slovaca

Abstract

The notion of a relatively uniform convergence (ru-convergence) has been used first in vector lattices and then in Archimedean lattice ordered groups.

Let G be an Archimedean lattice ordered group. In the present paper, a relative uniform completion (ru-completion) \( G_{\omega _1 } \) of G is dealt with. It is known that \( G_{\omega _1 } \) exists and it is uniquely determined up to isomorphisms over G. The ru-completion of a finite direct product and of a completely subdirect product are established. We examine also whether certain properties of G remain valid in \( G_{\omega _1 } \). Finally, we are interested in the existence of a greatest convex l-subgroup of G, which is complete with respect to ru-convergence.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, SK-040 01, Košice, Slovakia

    Štefan Černák

  2. Institute of Mathematics, P. J. Šafárik University, Jesenná 5, SK-041 54, Košice, Slovakia

    Judita Lihová

  3. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, SK-040 01, Košice, Slovakia

    Judita Lihová

Authors
  1. Štefan Černák
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  2. Judita Lihová
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Correspondence to Štefan Černák.

Additional information

(Communicated by Anatolij Dvurečenskij)

This work was supported by Science and Technology Assistance Agency under the contract No. APVT-20-004104. Supported by Grant VEGA 1/3003/06.

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Černák, Š., Lihová, J. On a relative uniform completion of an archimedean lattice ordered group. Math. Slovaca 59, 231–250 (2009). https://doi.org/10.2478/s12175-009-0120-9

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  • DOI: https://doi.org/10.2478/s12175-009-0120-9

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